On a class of strongly hyperbolic systems

Abstract

In this paper we prove a well-posedness result for the Cauchy problem. We study a class of first order hyperbolic differential [2] operators of rank zero on an involutive submanifold of T^*Rⁿ⁺¹-{0} and prove that under suitable assumptions on the symmetrizability of the lifting of the principal symbol to a natural blow up of the “singular part” of the characteristic set, the operator is strongly hyperbolic.